1949: THE HEINLEIN CALENDAR
Robert A. Heinlein's 1949 novel Red Planet
contained a brief reference concerning a Martian calendar. In
the course of a conversation in Chapter 1:
Jim thought back over the twenty-four months of the Martian year. "Since along toward the end of Zeus, nearly November."
"And now here it is the last of March, almost Ceres, and the summer gone."
From this it is clear that Heinlein's calendar comprised the twelve
Roman months of the Gregorian calendar, and with these were alternated
twelve new months whose names were taken from Greek and Roman
mythology. The fact that Heinlein's characters were living in
the northern hemisphere of Mars also indicates that on his calendar,
March occurred at the end of the northern hemisphere's summer,
and therefore simultaneously at the end of the southern hemisphere's
winter. As with Lowell's system, this is
the opposite orientation to the Gregorian calendar on Earth. Other
passages in the book refer to sols of the week with their familiar
terrestrial names, implying that Heinlein's Martian calendar also
incorporated the conventional seven-sol week.
Alfred Bester won the Hugo Award for The Demolished Man.
While the novel is set in 2301 A.D. New York City and has nothing
to do with Mars, in the first chapter the protagonist glances
at a clock giving "the time panorama of the solar system."
The dials read "February 15, 0205 Greenwich" for Earth
and "Duodecember 35, 2220 Central Syrtis" for Mars.
Ray Bradbury used the Gregorian calendar for his chronology in
The Martian Chronicles, and
spoke of August 1999 as being summer on Mars, which it will indeed
be in the northern hemisphere. However, Bradbury also had the
following spring as occurring in April 2000, when in factit will
still be the dead of winter in the northern hemisphere and the
height of summer in the southern hemisphere. From this it appears
that Bradbury mistakenly synchronized the Martian seasons with
the seasons of Earth.
1951: THE CLARKE CALENDAR
Arthur C. Clarke made a passing reference near the end of Chapter
8 of The Sands of Mars which definitely
implies a twelve-month Martian calendar incorporating seven-sol
Gibson had not yet mastered the intricacies of the Martian calendar, but he knew that the week-days were the same as on Earth and that Monday followed Sunday in the usual way. (The months also had the same names, but were fifty to sixty days in length.)
For quite a long time, the fact that Clarke's months varied between
fifty and sixty sols puzzled me. The few writers on the subject
of Martian timekeeping that I had discovered at this point, as
well as, had devised their calendars such that, if they had months
in them, they were of even length. Why weren't Clarke's as well?
Eventually it occurred to me that Clarke might have meant his
months to represent the passage of Mars through equal arcs of
thirty degrees in its elliptical orbit around the Sun. I made
some calculations to check this idea and found that near perihelion
Mars passes through a thirty degree arc in 46 sols, while near
aphelion such an angle requires 67 sols. A variation on this idea
would be to have the Martian months correspond to the passage
of that planet through the same heliocentric longitude (relative
to the Martian vernal equinox) as Earth does during the same months,
in effect unevenly stretching the Gregorian calendar to fit the
larger and more eccentric orbit of Mars. Clarke's comments seemed
to make a rough cut at this idea without bogging his readers down
in details. It is a curious coincidence that just as I hit upon
this idea, Makoto Nagatomo was writing a letter to the British
Interplanetary Society in response to my July 1988 Spaceflight
article "The Lost Calendars of Mars". As I was to shortly
discover, and as I will later discuss in this paper, the months
on Nagatomo's calendar are indeed based
on stretching the Gregorian calendar, and in retrospect, it is
possible that Heinlein's were as well.
Nagatomo's correspondence was followed a month later by a letter
from George E. Henry, who it turned out had
also devised a Martian calendar based on the same idea. Recently,
Frank Bauregger developed yet another
"stretched Gregorian" calendar. So far as I know, the
Zubrin calendar is the only example of an
1954: THE LEVITT CALENDAR AND THE LEVITT-MENTZER CLOCK
While searching for the details of what at the time I believed
to be Richardson's calendar (but was actually Aitken's),
I discovered evidence of yet another lost Martian calendar --
and the first construction of a Martian clock -- invented by his
contemporary I. M. Levitt. I also subsequently found that in addition
to describing the Aitken calendar, Richardson
mentioned the Martian calendar devised by Levitt in a footnote
of Exploring Mars.
Levitt published his idea of a Martian calendar in the May 1954 issue of Sky & Telescope
and later in Appendix 1 of his 1956 book, A Space Traveller's Guide to Mars.
He devised yet a different method of intercalation from those
discussed by Richardson and the one adopted by Aitken.
He specified a five-year sequence in which the first and fourth
years were 668 sols long and the other three years contained 669
sols. Additionally, however, Levitt allowed for the omission of
a leap sol every 1,000 years and therefore claimed for his calendar
an accuracy of one sol in 20,000 years.
Despite the fact that the lunar cycle, the natural basis for the
month as a unit of time, has nothing at all to do with Mars, Levitt
saw that the month was nevertheless a very desirable unit of time
to transplant to Mars. However, instead of having the Martian
months approximate the lunar cycle (about 29 Martian solar days)
and thus having more months in the longer Martian year, Levitt
proceeded along a different line of reasoning and instead divided
the Martian year into twelve months, as do most calendars on Earth.
Levitt's months are thus nearly twice as long as the months on the Gregorian calendar, averaging just slightly less than 56 sols each.
Of all the Martian solar calendars ever devised, Levitt's is one
of the most conservative. He retained the same names of the twelve
months of the year that date back to ancient Rome. The Levitt
calendar inherited the seven-day week from the Gregorian calendar,
and also preserved the Anglicized names of the seven days of the
week. There is on his calendar, however, an interesting departure
from the convention of the Gregorian calendar which makes it superior
to the Gregorian calendar and also gives it a definite advantage
over the Aitken calendar. As with Aitken's
calendar, Levitt's divides the Martian year into equal quarters
of 167 sols, except in the case of the last quarter of a 669-sol
year, which is 168 sols. But as opposed to Aitken,
who employed unvarying seven-sol weeks throughout his calendar
so that the sols of the week slid backward from quarter to quarter,
Levitt contrived a six-sol week to end each 167-sol quarter. Levitt's
six-sol weeks end with Friday and are immediately followed by
Sunday. As a result, every month on the Levitt calendar begins
with a Sunday, the first sol of the week, and thus his calendar
is perpetual over a 56-sol period (refer to the table).
Any given sol of the week can only occur on precisely eight dates
of the month; "If it's Tuesday, this must be the 3rd, or
the 10th, or the 17th, et cetera." This would be as easy
to memorize as multiplication tables.
While Aitken did not designate a beginning
year for his calendar, Levitt did, and thus his calendar can be
correlated to Earth's Gregorian calendar. In the absence of any
Martian historicalevent on which to base a Martian calendar, Levitt
tied the beginning of his Martian chronology to the beginning
of the Julian Period. Levitt began his Martian chronology with
the year 0 rather than 1. Thus 1 January 4713 B.C. on the Julian
calendar was also 1 January 0 M.Y. (Martian Year) on the Levitt
calendar. Although Levitt did not furnish an exact correlation
between his calendar and a modern date on the Gregorian calendar
in his May 1954 Sky & Telescope
article, he did state that 1 January 1954 A.D. occurred in the
year 3641 M.Y.
Levitt also considered the problem of reducing the Martian sol into smaller units of time. His idea was a simple one, and it has been duplicated many times since by other writers. Levitt divided the sol into 24 hours, and these were further broken down into units of 60 minutes with each minute in turn containing 60 seconds, just as we do on Earth. Of course, since the Martian solar day is 2.7 percent longer than the terrestrial solar day, each of these Martian units of time are proportionately longer in duration. This difference is so slight that, without actually comparing two chronometers each calibrated to the timekeeping system of the respective planet, one would indeed be hard pressed to notice the difference (if a Martian tells you that he'll be there in a minute, are you really going to notice if he slows up about three seconds late?).
Levitt turned his ideas on Martian timekeeping into actual hardware,
thereby creating the first operational system of Martian time.
Designed by Levitt and constructed in the home workshop of Ralph
B. Mentzer of the Hamilton Watch Company, the Earth-Mars clock
was unveiled at the Waldorf-Astoria Hotel in New York on 14 February 1954.
The main dial of the clock displayed the time of "sol"
on Mars; whether or not this was intended to be Martian Prime
Meridian Time is unclear. Additionally, the clock had three smaller
dials on its face: the first marked the sol, month, and year on
Mars according to the Levitt calendar; the second displayed 24-hour
Greenwich Mean Time; the third showed the day, month, and year
according to the Gregorian calendar. The Levitt-Mentzer clock
was capable of being run forward or backward at 2,000 times normal
speed and stopped at any date between 1 January 1970 and 31 December
1989, and thus functioned as a mechanical analog computer for
relating time on both worlds. Recall that at the time Levittand
Mentzer devised their clock, electronic digital computers were
cumbersome, expensive, and still quite rare.
An HTML version of Levitt's article, "Mars Clock and Calendar", and of the 15 February 1954 New York Times story, "Mars Clock in Debut", are available on the Martian Time Web Site.
Carl Jacobi's short story "The Martian Calendar"
revolves around a mysterious Martian mechanism which not only
measures the passage of time, but apparently alters it as well.
However, the story describes only one detail of the Martian timekeeping
system, and it is dead wrong. Unfortunately, Jacobi was under
the mistaken impression that the Martian year lasts 687 Martian
sols, thereby repeating the error that Burroughs
committed nearly half a century before.
1957: THE PIPER CALENDAR
When Terran archaeologists identify a periodic table in the ruins
of an ancient Martian university in H. Beam Piper's "Omnilingual",
it serves as a Martian Rosetta Stone, allowing Terrans to transliterate
a portion of the Martian language for the first time. In the course
of this absorbing tale the archaeologists learn that the Martians
divided their "masthar" (year) into ten more or less
equal "mastharnorvod" (months). It is disclosed that
the name of each month is simply the number of its order in the
calendar year, which calls to mind the Roman calendar's Quinctilis
(later Julius), Sextilis (later Augustus), Septembris, Octobris,
Novembris, and Decembris. The names of only six of these Martian
months are given: Trav (first), Sanv (second), Krav (third), Doma,
fifth), Yenth (eighth), and Nor (tenth).
Weeks were not mentioned in Piper's story, but since one may presume
that each month contained either 66 or 67 sols, the division of
each month into eleven six-sol weeks would be a logical development.
One can also speculate that, rather than having each month begin
haphazardly on any sol of the week as the Gregorian calendar does,
the Martians might have taken advantage of the nearly perfect
division of each month by six, thus choosing instead to treat
the 67th sol of the month as an intercalary sol and allowing each
month to begin on the first sol of the week (refer to the table).
Of course, this is only speculation, but it does illustrate that
a six-sol week could work quite well on Mars.
1966: THE COMPTON CALENDAR
In Chapter 1 of D. G. Compton's Farewell Earth's Bliss,
one of the transportees to the penal colony on Mars passed the
time on the voyage by speculating on the structure of the Martian
Fifty-seven days hath September,
April, June, and November.
All the rest have fifty-eight,
Save poor February's fate,
Having fifty-three days clear,
And fifty-two in each Leap Year.
Nobody on board had any real idea how the people in the settlement would have organised their six-hundred-and-eighty-seven-day year.
Evidently! Once the new convicts reached Mars, they should have
discovered that the Martian year was really only 668 sols. By
the end of the novel, most of them had run out of time anyway.
1967: THE HENRY CALENDAR
Up until now, all of the calendars I have discussed that were
developed beyond mere passing references from novels or short
stories have been constructed on equal divisions of the Martian
year. On the other hand, the Clarke calendar,
with its months varying between fifty and sixty sols, seems to
have been based instead on months corresponding to the movement
of Mars through roughly the same arcs as their counterparts on
Earth, or approximately thirty degrees. The 24-month Heinlein calendar
may also have embodied this concept (fifteen-degree arcs in this
case), since the summer was gone at the end of March and therefore
the autumnal equinox would presumably occur in early Ceres (the
sixth month), and one can further surmise that the winter solstice,
vernal equinox, and summer solstice would fall early in the twelfth,
eighteenth, and twenty-fourth months, respectively.
George E. Henry, writing in his regularly appearing column in
the Daytona Beach Morning Journal,
approached the subject of a Martian calendar from this same direction.
Starting with twelve months as did Clarke,
and choosing a northern hemisphere bias as opposed to Heinlein's
southern bias, Henry essentially stretched the Gregorian calendar
to fit the Martian year so that the vernal equinox, the summer
solstice, autumnal equinox, and winter solstice would take place
in late March, June, September, and December, respectively, just
as they do on Earth. His calendar perpetuates the flaws of the
terrestrial model on which it is based. The months begin haphazardly
on varying days of the week, as do the years, and thus it is not
perpetual. He even kept the leap-sol at the end of February, instead
of placing it at the end of the year where it would make more
sense. After all, February was originally made the month of variable
length when it was the last month of the Roman calendar rather
than the second (at that time, September was the seventh month,
as its name implies!).
Since Henry had to write his newspaper column to a tight space
constraint and to a general audience (which of course had to be
given a quick lesson in the pertinent astronomical concepts within
that tiny space), his description of a Martian calendar was necessarily
brief and lacking in detail. He did touch on the subject of intercalation,
noting that six out of every ten years must be a leap year, but
did not specify a sequence for these. There was no correlation
given for a specific date on his calendar and a corresponding
1976-1982: THE VIKING NUMERICAL CHRONOLOGY
The first practical need for a Martian calendar of even a rudimentary
form, and for a system of time based on Martian solar days rather
than terrestrial solar days, began with the landing of the Viking
1 spacecraft, when project members began expressing Martian
solar days as "sols". The sol of the landing, 20 July
1976, they designated "Sol 0", and the sols that followed
were numbered successively. With the landing of this first unmanned
spacecraft, humans began working on the surface of Mars, albeit
by proxy. Thus it was that humans began working by Martian time,
working their daily schedules around the daylight hours at the
two Viking lander sites. This was the true beginning of Martian
chronology, for although the Levitt-Mentzer
clock was constructed more than two decades earlier, it was apparently
never used as much more than a planetarium exhibit.
1977: THE MOORE CALENDAR
The Viking invasion of Mars inspired an invasion of the bookstands
by a host of books about Mars. One of them was Patrick Moore's
1977 revision of Guide to Mars,
and in it was a description of yet another Martian calendar. Moore's
idea was to divide the Martian year into 18 months, all but three
of which would be 37 sols long. The 6th, 12th, and 18th months
were instead 38 sols long. Moore made no mention of weeks in his
calendar, and indeed, since 37 is a prime number, there is no
hope of having an integral number of weeks -- seven-sol weeks
or otherwise -- in his months, as Levitt
had in his calendar. Neither could the Moore calendar approach
the equally elegant solution of the Aitken calendar's
two-year cycle. Yet the sociological need for the week as a unit
of time is incontrovertible, and certainly the Martians will not
do without it. Apparently, then, the Moore calendar
would suffer from the same lack of rational correlation between
weeks and months that plagues the Gregorian calendar. Also, Moore
did not take on the problem of intercalation to account for the
fractional number of sols in the year.
1977: THE ROHRER CALENDAR
William G. Rohrer’s paper "Systemy Czasu Zlawiska Zwiazane z Czasem na Marsie" appeared in the Polish publication Posepy Astronautyki. He miscalculates the length of the Martian year, arriving at the figure of 667.620 sols, while the length of the Martian tropical solar year is 668.5921 sols. It is also worth noting that Rohrer has a record four different lengths of calendar years, which is rather cumbersome. His intercalation formula is:
|Odd-numbered years||667 sols|
|Even-numbered years||668 sols|
|Years divisible by 10||669 sols|
|Years divisible by 50||670 sols|
Rohrer's 19 months, which are designated by Greek letters, are of a uniform length of 35 sols, and since he retains the seven-sol week, as a consequence, his calendar is of the fixed-week type. However, the fact that 19 is a prime number obviously means that his calendar year cannot be divided by any other number while simultaneously dividing into an integral number of months. Since 19 x 35 = 665, the residual sols, either 2, 3, 4, or 5, occur outside of the seven-sol week. I am not fluent in Polish, so I am only guessing that these residual days occur at the end of the year, in similar fashion to the Coptic calendar.
The Rohrer calendar year begins on the southern hemisphere’s vernal equinox, that is to say, the northern hemisphere’s autumnal equinox. His calculation of the length of the Martian seasons also contains some errors. The values he gives are:
Rohrer provides no epoch for his calendar.
1979: THE NAGATOMO CALENDAR
Makoto Nagatomo, of the Institute of Space and Astronautical Sciences
in Japan, happened to independently develop the same approach
as Henry's, that of Martian months spanning
the same arcs of the Martian orbit as their Terran counterparts
with respect to Earth's orbit. Nagatomo's treatment of the subject
also went to about the same depth as Henry's,
since his ideas on Martian timekeeping appeared only as an ancillary
discussion in his short story, "High-Speed Mars Railway",
which was published in the Winter 1979 issue of Uchu Jidai.
As with the Henry calendar, Nagatomo did
not design his to be perpetual, nor did he include in his story
and reference dates to correlate his calendar with the Gregorian
calendar, nor did he entertain any thoughts on intercalation.
At this point, I decided to devise my own "stretched Gregorian" calendar.
My results seem to indicate that both the Henry
and Nagatomo calendars are out of phase by about a month. Henry's
longest month is June and his shortest is December, while Nagatomo's
July is longer that his June by only a sol and both his November
and December contain 48 sols. According to my results, aphelion
should occur in late May, making it the longest month, and perihelion
should happen in late November, causing it to be the shortest
1984: THE LOVELOCK-ALLABY CALENDAR AND CLOCK
James Lovelock and Michael Allaby contributed some thoughts on
Martian timekeeping in their 1984 book The Greening of Mars.
They divided the sol into the conventional 24-hour, 60-minute,
and 60-second system, just as Levitt did. Although Lovelock and
Allaby noted the correct length of the Martian solar day as 24
hours 39 minutes 35 seconds, and intended that their Martian calendar
be based on the Martian solar year, they made the mistake of having
687 sols in their calendar when this is in fact the number of
terrestrial solar days in a Martian solar year. A popularly written
mixture of fact and speculation told in the format of a narrative
by a fictional citizen of Mars of the twenty-third century, The Greening of Mars
informs the reader:
Mars has a year of 687 days. To be more precise, it is 686.9804 days, which means we have 'leap years' every so often to keep the calendar straight. Our 'leap years' are not like those of Earth, though, which is why I use the expression in quotation marks. On Mars leap years come every fifty-one years, and we lose a day.
It was obvious to Lovelock and Allaby that the cycles of Phobos
and Deimos are entirely unsuitable as the bases for units of time.
But, whereas others chose to adopt some artificial chronometric
unit to divide up the Martian year into anywhere from ten to 24
parts, there are no months at all in the Lovelock-Allaby calendar:
We do not count months. On Earth these are based, clumsily, on the orbit of the Moon. Indeed, we have two tiny moons that look about the size Venus looks when seen from Earth. A division of the year into months would force us to choose one in preference to the other, and that would cause endless wrangling among the Phobos and Deimos factions that would spring up instantly. Even then it would not be easy. Phobos orbits Mars three times each day, and Deimos takes rather more than a day to make a single orbit. Martian months would be rather different from terran months! Perhaps we could use both and try to devise a double-month system. I cannot begin to imagine what that would be like.
Recognizing the sociological necessity of the seven-day week,
Lovelock and Allaby adopted this unit of time which has no astronomical
analogue either on Earth or Mars. Their calendar thus consists
of sols, weeks, and years. They retained the same names of the
sols of the week that are used on Earth, and the weeks themselves
were numbered from the beginning to the end of the year. As their
fictional character explains:
My date of birth, for the record, was 3.68.06. That is to say, I was born on the third day (which we call Tuesday, as I said) of the sixty-eighth week of the sixth year of the century. We omit the number of the century, but I was born in the year 106.
Lovelock and Allaby chose to begin their Martian chronology with
the establishment of the first human outpost on Mars. They were
unclear as to whether they intended the anniversary of this event
to be New Year's Day on their calendar, or if this would merely
define the first year of the calendar while New Year's Day would
be fixed by some other occurrence such as the vernal equinox.
In any case, since the beginning of their chronology is defined
by an event which has yet to come about, their calendar cannot
be referenced to the Gregorian calendar. The table shows the Lovelock-Allaby
calendar corrected for the 668.6-sol year.
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